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Properties

Label 1176.4.v
Level $1176$
Weight $4$
Character orbit 1176.v
Rep. character $\chi_{1176}(275,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $944$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1176.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1176, [\chi])\).

Total New Old
Modular forms 1376 976 400
Cusp forms 1312 944 368
Eisenstein series 64 32 32

Trace form

\( 944 q + 2 q^{3} + 2 q^{4} + 20 q^{6} + 2 q^{9} + O(q^{10}) \) \( 944 q + 2 q^{3} + 2 q^{4} + 20 q^{6} + 2 q^{9} - 30 q^{10} + 2 q^{12} - 238 q^{16} + 4 q^{18} + 4 q^{19} + 364 q^{22} + 224 q^{24} - 10996 q^{25} + 8 q^{27} - 338 q^{30} + 110 q^{33} + 256 q^{34} - 396 q^{36} + 498 q^{40} - 32 q^{43} + 1056 q^{46} + 416 q^{48} - 914 q^{51} - 600 q^{52} + 1420 q^{54} - 124 q^{57} - 2622 q^{58} - 320 q^{60} - 916 q^{64} - 1198 q^{66} - 3260 q^{67} + 2878 q^{72} - 212 q^{73} + 144 q^{75} + 3496 q^{76} - 20 q^{78} - 614 q^{81} + 3412 q^{82} - 4274 q^{88} + 3736 q^{90} - 2604 q^{94} - 4274 q^{96} + 4672 q^{97} + 2900 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)